What are the differences between proxying and parenting in ManuelLab?
In ManuelLab, you may Proxy items to the mesh before Finalization. This means it will share the same origin point as the body, and when you pose the body and fit the proxy ater calibration, it will match the pose by location.

I am raising this topic because, time and time again, I have tried proxying clothes to the mesh, and while it worked and did exactly what it was supposed to, the sleeves also twisted with the arms, which is unnatural with clothes.

Parenting is much the same as proxying, only it moves as the skeleton does, not after fitting the proxy. They are quite similar, yes. However, when trying to do this with cloth meshes, use the play button to run a simulation (make sure to raise the frame count) and avoid proxying. This is especially meaningful for long-sleeved clothes. Short-sleeved clothes will be mostly fine.

This is no attempt to defame proxying (or even parenting), as I have found it plenty useful, but I have learned to keep in mind how cloth meshes will look, even to my absent-minded dismay, when proxying and expecting the ends to not twist around.
At this time, I am not sure if proxying works with motion capture, but I wager it would be plenty fantasic and useful if it does.